Economists have recently revived the notion that recessions play a useful role in fostering innovation and growth. But in practice, a major source of innovation, R&D, is procyclical. In fact, R&D is procyclical even for firms that do not appear to be financially constrained. This paper argues the reason R&D is procyclical is because of a dynamic externality inherent to R&D that makes entrepreneurs short-sighted and concentrate their innovation in booms even though it is optimal to concentrate it in recessions. Thus, what previous authors have argued is a desirable feature of fluctuations in the previous literature — creating opportunities for intertemporal substitution — turns out to be a social liability in equilibrium.